Information theory usually models a communication channel by a conditional probability distribution. For example, a model for communicating a symbol from one point to another might involve the conditional probability distribution PY|X(•) that evaluates to:PY|X(b|a), aεX,bεY,  (1)where X and Y are random variables taking on values in the discrete and finite alphabets X and Y, respectively. The aim of communication is to transmit reliably a message index W taking on one of M values from a transmitter to a receiver. Suppose that to accomplish this task one transmits a string of n symbols Xn=X1, X2, . . . , Xn over the channel. The rate of communication is thenR=log2(M)/n  (2)Bits per channel use. The maximum rate C at which one can transmit reliably is called the capacity of the channel.
A relay channel is a multiterminal channel with three parties or nodes: a transmitter (node 1), a relay (node 2), and a receiver (node 3). A possible model for relaying might involve the probabilitiesPY2Y3|X1X2(b2,b3|a1,a2),  (3)where X1 is the transmitter's channel input, Y3 is the receiver's channel output, and X2 and Y2 are the relay's input and output, respectively. The idea is that the transmitter and receiver can only transmit and receive, respectively, but the relay can both transmit and receive. Suppose that the transmitter and relay transmit the strings X1n=X11, X12, . . . , X1n and X2n=X21, X22, . . . , X2n, respectively, over the channel. Suppose further that the relay can react quickly so that its input X2i can be any function of its past outputs Y2i−1. The relay channel is said to be memoryless if one hasPY2iY3i|WX1iX2iY2i−1Y3i−1(b2i,b3i|ω,a1i,a2i,b2i−1,b3i−1)=PY2Y3|X1X2(b2i,b3i|a1i,a2i)  (4)for all a1i, a2i, b2i, b3i, and i=1, 2, . . . , n. Only memoryless channels will be considered. Again, the maximum rate C at which one can transmit reliably is called the capacity of the channel.
A relay network is a generalization of a relay channel to a system with T nodes: a transmitter (node 1), T-2 relays (nodes 2 to T-1), and a receiver (node T). A model for relaying would involve the probabilitiesPY2Y3. . . YT|X1X2. . . XT−1(b2,b3, . . . bT|a1,a2, . . . ,aT−1).  (5)The relay network is memoryless if the natural extension of the condition (4) is true, that is, if the ith channel outputs Yti, t=2,3, . . . , T, depend only on the ith channel inputs Xti, t=1, 2, . . . , T−1, given the message, the present (or ith) and past channels inputs, and the past channel outputs. The capacity C is again the maximum rate at which one can transmit reliably.
Several types of relaying strategies may be employed in relay channels or networks. In an amplify-and-forward strategy, the relay amplifies the most recent Y2. More generally, the relay transmits some function of a small number of the past Y2. In a compress-and-forward strategy, the relay quantizes, compresses, and channel encodes a string of Y2 and transmits the resulting quantized values digitally to the receiver. A more sophisticated quantization exploits the statistical dependence between Y2 and Y3 to reduce the compression rate. In these systems, the transmitter transmits and the relay is silent in a first block, and then the transmitter is silent and the relay transmits in a second block. This mutually exclusive transmitting between the transmitter and the relay typically causes the transmission rate of the transmission system to suffer.
Accordingly, what is needed in the art is a way to overcome the limitations of the current art.